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Given y=e^5x*sin2x, what is dy/dx?

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bibiloi | Student, Undergraduate | (Level 3) Honors

Posted August 21, 2011 at 12:01 AM via web

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Given y=e^5x*sin2x, what is dy/dx?

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giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted August 21, 2011 at 12:06 AM (Answer #1)

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We'll have to use two important rules to determine the derivative of the given function: theproduct rule and the chain rule.

The product rule:

(u*v)' = u'*v + u*v'

Let u = `e^(5x)` . To differentiate with respect to x, we'll have to use the chain rule:

u' = `e^(5x)` *(5x)'

u' = 5`e^(5x)`

Let v = sin 2x. By the chain rule, we'll get: v' = 2cos 2x.

dy/dx = 5`e^(5x)` *sin 2x + 2 `e^(5x)`*cos 2x

dy/dx = `e^(5x)` (5 sin 2x + 2 cos 2x)

Therefore, the requested derivative of the given function is:

dy/dx = `e^(5x)` (5 sin 2x + 2 cos 2x)

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